Mixture Decomposition for Distributions from the Exponential Family using A Generalized Method of Moments

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A finite mixture distribution consists of the superposition of a finite number of component probability densities, and is typically used to model a population composed of two or more subpopulations. Mixture models find utility in situations where there is a difficulty in directly observing the underlying components of the population of interest. This paper examines the method of moments as a general estimation technique for estimating the parameters of the component distributions and their mixing proportions. It is shown that the same basic solution can be applied to any continuous or discrete density from the exponential family with a known common shape parameter. Results of an empirical study of the method are also presented.